Abstract
For a sequence of finite Markov chains ${\cal L}(N)$ we introduce the notion of "convergence time to equilibrium" $T(N)$. For sequences that are obtained by truncating some countable Markov chain ${\cal L}$ we find the convergence time to equilibrium in terms of Lyapunov function of Markov chain ${\cal L}$. We apply this result to queueing systems with a limited number of customers: a priority system with several customer types and the Jackson network.
Key words: convergence time to equilibrium, Lyapunov functions, nonreversible Markov chains, Monte Carlo Markov chains, priority systems, Jackson network.
Submitted to Fundamental and Applied Mathematics.
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